When is every non central-unit a sum of two nilpotents?

2021/01/14 by Breaz, Simion, Zhou, Yiqiang
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2101.05449

Abstract

A ring is said to satisfy the 2-nil-sum property if every non central-unit is the sum of two nilpotents. We prove that a ring satisfies the 2-nil-sum property iff it is either a simple ring with the 2-nil-sum property or a commutative local ring with nil Jacobson radical, and we provide an example of a simple ring with the 2-nil-sum property that is not commutative. Moreover, a simple right Goldie ring has the 2-nil-sum property iff it is a field.

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• Rings Whose Non-Invertible Elements Are Nil-Clean
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